Georg, Peter and Grasedyck, Lars and Klever, Maren and Schill, Rudolf and Spang, Rainer and Wettig, Tilo (2023) Low-rank tensor methods for Markov chains with applications to tumor progression models. JOURNAL OF MATHEMATICAL BIOLOGY, 86 (1): 7. ISSN 0303-6812, 1432-1416
Full text not available from this repository. (Request a copy)Abstract
Cancer progression can be described by continuous-time Markov chains whose state space grows exponentially in the number of somatic mutations. The age of a tumor at diagnosis is typically unknown. Therefore, the quantity of interest is the time-marginal distribution over all possible genotypes of tumors, defined as the transient distribution integrated over an exponentially distributed observation time. It can be obtained as the solution of a large linear system. However, the sheer size of this system renders classical solvers infeasible. We consider Markov chains whose transition rates are separable functions, allowing for an efficient low-rank tensor representation of the linear system's operator. Thus we can reduce the computational complexity from exponential to linear. We derive a convergent iterative method using low-rank formats whose result satisfies the normalization constraint of a distribution. We also perform numerical experiments illustrating that the marginal distribution is well approximated with low rank.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SIGNALING PATHWAYS; MATRIX; APPROXIMATION; ALGORITHMS; FORMULATION; Transient distribution; Stochastic Automata Networks; Mutual Hazard Networks; Hierarchical Tucker format |
| Subjects: | 000 Computer science, information & general works > 004 Computer science |
| Divisions: | Medicine > Institut für Funktionelle Genomik > Lehrstuhl für Statistische Bioinformatik (Prof. Spang) Informatics and Data Science > Lehrstuhl für Statistische Bioinformatik (Prof. Spang) Physics > Institute of Theroretical Physics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 11 Mar 2024 15:11 |
| Last Modified: | 11 Mar 2024 15:11 |
| URI: | https://pred.uni-regensburg.de/id/eprint/59676 |
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